Aristotle on Deduction and Inferential Necessity

Aristotle on Deduction and Inferential Necessity

Article excerpt

Aristotle's Topics introduces a deductive argument as follows: "a deduction [sullogismos] is an account [logos] in which, some things being supposed, something other than that which is assumed results of necessity [ex anagkes sumbainei] in virtue of that which has been assumed." (1) The translation of sullogismos as "deduction," instead of "syllogism," is a matter for discussion, but the term "deduction" here exclusively pertains to Aristotle's conception of deduction in the same way as epagoge, translated as "induction," is confined to his view on induction. We then avoid Keyt's criticism that the word "deduction" fails to assert the difference between a syllogism and the modern notion of deduction. (2) As for logos, its translation as "account," instead of "argument," aims to stress the role of deduction in language. Indeed, the first meaning of logos is "sentence" in spoken language, as explained in De Interpretatione. (3) The Topics does not explain further the notion of deduction, as it immediately focuses on the distinction between demonstration and dialectical deduction, namely the contrast between knowledge and opinion.

On the other hand, the Prior Analytics is concerned with deductions simpliciter, which are neither demonstrative nor dialectical. (4) Aristotle suggests a same formulation of deduction, despite the slightly different wording: "a deduction is an account in which, some things being supposed, something other than that which is assumed results of necessity [ex anagkes sumbanei] in virtue of these being so." (5) A deduction simpliciter is a necessary inference from given premises. Aristotle adds: "I mean by 'these being so' [toi tauta einai] that which results because of these, and I mean by 'that which results because of these' that which stands in need of no term outside in order for that which is necessary to be produced." (6) An inference is necessary when the conclusion is drawn from the terms of the premises alone, without referring to anything outside of them. Thus, a conclusion is deducible when it has been necessarily inferred from its premises. If two distinct conclusions were inferred from the same premises, the two inferences could not be necessary, since a necessary inference cannot be otherwise. If no conclusion "results of necessity" (ex anagkes sumbainei) from the premises, then the account cannot be a deduction.

Modern logicians, in their logical reevaluation of Aristotle's deductive system, are very reluctant to speak of inferential necessity. Lukasiewicz is the first to suggest a modern reconstruction of Aristotelian logic by identifying a syllogism with a universalized conditional proposition, such that the logic of syllogisms amounts to a system of true propositions. (7) He understands "syllogistic necessity" as a universal quantifier: "the Aristotelian sign of syllogistic necessity represents a universal quantifier and may be omitted, since a universal quantifier may be omitted when it stands at the head of a true formula." (8) Lukasiewicz is not interested in Aristotle's inferential necessity and replaces it with a notion compatible with his own logical reconstruction. In contrast, Patzig attempts to underline the importance of necessity in Aristotle by distinguishing two kinds of necessity, that is, relative or absolute necessity. (9) His explanation, however, makes sense only in the context of Lukasiewicz's logical reconstruction, since Patzig understands Aristotle's syllogism as a true conditional proposition.

Nowadays, it is standard to identify Aristotle's inferential necessity with logical validity. For instance, Keyt writes: "the conclusion of a syllogism follows 'of necessity' from its premises: only valid arguments are syllogisms." (10) An argument is valid if its premises logically entail its conclusion. This logical reconstruction is based on a criticism of Lukasiewicz, initiated by Corcoran and Smiley, such that the logical truth of a conditional proposition is replaced with the logical validity of a natural deduction. …